1) Field of the Invention
This invention relates to a technique for evaluation after estimating, by a numerical analysis, the strength at a spot welded portion of a structure formed from a plurality of panels spot welded at a plurality of locations such as, for example, the body of an automobile.
2) Description of the Related Art
In recent years, a technique for numerically analyzing the strength of a structure using a computer has been developed and utilized in order to satisfy such demands as a demand for reduction of the period of development of a structure and a demand for reduction of the cost for development. It is known that the finite element method is useful as such a technique for an analysis of the strength of a structure as just described.
A structure is sometimes formed from a plurality of panels spot welded to each other at a plurality of locations, for example, like the body of an automobile. In order to use a computer to analyze the strength of a structure of the type just described, a spot welded portion is modeled, and the finite element method is applied to the model. Several methods have been developed for modeling a spot welded portion so as to allow the finite element to be used for the calculation, and for example, a beam coupling model, a shared nodal point model, a cobweb model, an RBE3 model, a solid model and a shared side model are known.
FIGS. 11(a) to 11(c) show different examples of a beam coupling model. Referring to FIGS. 11(a) to 11(c), each of the beam coupling models shown is obtained by modeling a plurality of panels 11 and 12 as being coupled to each other at a spot welded location by a beam element 13. Each of the panels 11 and 12 coupled to each other by the beam element 13 is suitably divided into elements, and the finite element method is used to perform an analysis with regard to the strength in a unit of an element obtained by the division. At this time, each of the beam element 13 and the portions of the panels 11 and 12 coupled to the beam element 13 is generally handled as a solid element.
Incidentally, according to the modeling methods mentioned above, in order to allow accurate description of an event wherein a solidified portion formed across a plurality of panels by welding transmits a bending moment from one to another one of the panels, the configuration of the model must be complicated, and much time is required for production of the model. On the contrary, if the configuration of the model is simplified so as to allow the model to be produced in a short period of time, then an event around a spot welded portion cannot be analyzed accurately.
Therefore, techniques have been developed wherein a fine model is formed for each location for which a high degree of analysis accuracy is required while a rough model is formed for any other portion so that an event around a spot welded portion can be analyzed accurately while the time required for modeling is reduced.
For example, a technique is proposed in a Patent Document 1[Japanese Patent Laid-Open No. 2002-35986] wherein a shared nodal point model is used to produce a simple model of a spot welded portion and is used to execute the finite element method, and thereafter, a value corresponding to a peeling distance in a direction perpendicular to the plane is calculated and then compared with a predetermined value to select a location at which the peeling distance is comparatively great and then a detailed model is produced for the selected location. In short, although a simple model having a low degree of analysis accuracy is used, since a great peeling distance is calculated at a spot welded location at which the degree of danger is high while a small peeling distance is calculated at another location at which the degree of danger is low, it can be discriminated accurately whether or not a detailed model is required depending upon the peeling distance.
Incidentally, when each of panels of a beam coupling model is divided into elements, various dividing manners are available as seen in FIGS. 11(a) to 11(c). In particular, the panels 11 and 12 may be divided into similar elements (usually rectangular elements) using a portion of each of the panels 11 and 12 coupled to the beam element 13 as a nodal point 14 as seen in FIG. 11(a). Or, the panels 11 and 12 may be divided into elements of different sizes from each other using a portion of each of the panels 11 and 12 coupled to the beam element 13 as a nodal point 14 as seen in FIG. 11(b). Or else, depending upon the shape of a portion around a spot welded portion, a mesh element of a different shape may be formed partially in the same panel 11 as seen in FIG. 11(c).
Where attention is paid to such manners of element division as described above, in order to reduce the time required for modeling while making it possible to accurately analyze an event around a spot welded portion as described above, since it is apparent that the danger in strength is high at a portion around a spot welded location, it is a generally possible idea to apply fine division to locations around spot welded locations while rough division is applied to the other portions.
Further, where it is tried to evaluate the strength of a panel including spot welded locations, various methods including, for example, a method wherein a stress intensity factor ΔKθmax (K value) of the fracture mechanics is used assuming a spot welded portion as an annular crack and another method wherein a nominal structural stress σM of a welding nugget portion determined using the elastic theory of a flat plate from six components of force of a spot element are available.
Incidentally, where the strength of a panel including a spot welded location is evaluated using arithmetic operation performed using a computer, it is a subject to be solved what analysis technique should be adopted and what division should particularly be adopted in the proximity of a welded location in order to achieve both of assurance of the accuracy in analysis and simplification of a model.
Where the method wherein a K value of the fracture mechanics described above is used in the analysis technique, if the K value can be estimated, then simplification of a calculation model can be achieved. However, in order to estimate the K value, a database which includes data of the K value for different modes of shearing, peeling and plane bending is required, and much time and labor are required for production of the database.
On the other hand, in the method which uses the nominal structure stress σM, although the number of elements is small and it is easy to examine a modified structure, the method is liable to be influenced by the difference in the input form, and the result of the analysis is liable to suffer from a significant dispersion.
As regards the division of elements, the cobweb model wherein a spot welded portion is described with a beam element, neighboring plate elements disposed in a fine density around the beam element and an element (for example, a solid element) having a rigidity higher than the other locations and positioned between the beam element and the neighboring plate elements for connecting them to each other is considered suitable as disclosed in the Patent Document 1 mentioned hereinabove. However, for example, where a stress value is used to perform an analysis, since those of the neighboring plate elements which are connected to the element having a higher rigidity than the other locations have stress values much higher than the other locations, the numerical analysis itself becomes difficult, and also the evaluation of a result of the analysis becomes difficult.
Further, for example, where a stress value is used to perform an analysis, it is necessary to perform the analysis in such a manner that a spot welded portion to which the cobweb model is applied and general elements neighboring the spot welded portion may be continuous to each other. In this instance, it is demanded to simplify element division as far as possible while the accuracy in analysis is assured.